Out of 10 countries — Country 1 through Country 10 — Country 9 has the highest gross domestic product (GDP), and Country 10 has the highest GDP per capita. GDP per capita is the GDP of a country divided by its population. The table below provides the following data about Country 1 through Country 8 for the year 2024.

• Column 1 gives the country’s identity.
• Column 2 gives the country’s GDP as a fraction of the GDP of Country 9.
• Column 3 gives the country’s GDP per capita as a fraction of the GDP per capita of Country 10.
• Column 4 gives the country’s annual GDP growth rate.
• Column 5 gives the country’s annual population growth rate.

Country	GDP	GDP per capita	GDP growth rate	Population growth rate
Country 1	0.15	0.41	0.20%	-0.12%
Country 2	0.14	0.25	0.90%	-0.41%
Country 3	0.13	0.02	6.50%	0.70%
Country 4	0.12	0.38	0.50%	0.49%
Country 5	0.1	0.36	0.70%	0.31%
Country 6	0.08	0.08	3.20%	0.61%
Country 7	0.08	0.3	0.70%	-0.11%
Country 8	0.07	0.41	1.20%	0.71%

Assume that the GDP growth rates and population growth rates of the countries will remain constant for the next three years.

Q. 1 Which one among the countries 1 through 8, has the smallest population in 2024?
1) Country 5 2) Country 8 3) Country 3 4) Country 7
Q. 2 The ratio of Country 4’s GDP to Country 5’s GDP in 2026 will be closest to
1) 1.314 2) 1.195 3) 0.963 4) 1.032
Q. 3 Which one among the countries 1, 4, 5, and 7 will have the largest population in 2027?
1) Country 4 2) Country 1 3) Country 7 4) Country 5
Q. 4 For how many countries among Country 1 through Country 8 will the GDP per capita in 2027 be lower than that in 2024?

Absolutely! Let’s go through each question in detail using the table provided.

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🔢 Understanding the Key Terms

• GDP per capita = GDP / Population
• All GDPs are given as a fraction of Country 9’s GDP.
• All GDP per capita values are given as a fraction of Country 10’s GDP per capita.
• So, for any country: Population (relative)=GDP (fraction)GDP per capita (fraction)\text{Population (relative)} = \frac{\text{GDP (fraction)}}{\text{GDP per capita (fraction)}}

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✅ Q.1: Which country has the smallest population in 2024?

We compute: Population fraction=GDP fractionGDP per capita fraction\text{Population fraction} = \frac{\text{GDP fraction}}{\text{GDP per capita fraction}}

Here are the values:

Country	GDP	GDP per capita	Population = GDP / GDPpc
Country 1	0.15	0.41	0.15 / 0.41 ≈ 0.366
Country 2	0.14	0.25	0.56
Country 3	0.13	0.02	6.5
Country 4	0.12	0.38	0.3158
Country 5	0.10	0.36	0.2778
Country 6	0.08	0.08	1.00
Country 7	0.08	0.30	0.267
Country 8	0.07	0.41	0.1707 ✅ Smallest

✅ Answer: Country 8

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✅ Q.2: GDP ratio of Country 4 to Country 5 in 2026

GDP in 2026 (after 2 years) = GDP₀ × (1 + r)²

• Country 4: GDP=0.12×(1+0.005)2=0.12×1.010025≈0.1212GDP = 0.12 × (1 + 0.005)^2 = 0.12 × 1.010025 ≈ 0.1212
• Country 5: GDP=0.10×(1+0.007)2=0.10×1.014049≈0.1014GDP = 0.10 × (1 + 0.007)^2 = 0.10 × 1.014049 ≈ 0.1014

Ratio: 0.12120.1014≈∗∗1.1952∗∗\frac{0.1212}{0.1014} ≈ **1.1952**

✅ Answer: Option 2) 1.195

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✅ Q.3: Which one among Country 1, 4, 5, 7 will have the largest population in 2027?

Population in 2027 = Population₀ × (1 + population growth rate)³

Country	Pop_2024	Pop Growth	Pop_2027
Country 1	0.366	-0.12%	0.366 × (0.9988)³ ≈ 0.3647
Country 4	0.316	0.49%	0.316 × (1.0049)³ ≈ 0.3217
Country 5	0.278	0.31%	0.278 × (1.0031)³ ≈ 0.2806
Country 7	0.267	-0.11%	0.267 × (0.9989)³ ≈ 0.2659

✅ Highest is Country 1 with ~0.3647

✅ Answer: Option 2) Country 1

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✅ Q.4: How many countries will have lower GDP per capita in 2027 than in 2024?

GDP per capita in 2027 is calculated as: GDP per capita2027=(1+GDP_growth)3(1+Pop_growth)3\text{GDP per capita}_{2027} = \frac{(1 + GDP\_growth)^3}{(1 + Pop\_growth)^3}

We check if this value is < 1, i.e., GDP per capita has decreased.

Let’s calculate for each:

Country	GDP G (%)	Pop G (%)	Ratio = (1+GDP)³ / (1+Pop)³
Country 1	0.2	-0.12	(1.002)³ / (0.9988)³ ≈ 1.0096 ✅
Country 2	0.9	-0.41	(1.009)³ / (0.9959)³ ≈ 1.040 ✅
Country 3	6.5	0.70	(1.065)³ / (1.007)³ ≈ 1.19 ✅
Country 4	0.5	0.49	(1.005)³ / (1.0049)³ ≈ 1.000 ✅
Country 5	0.7	0.31	≈ 1.01 ✅
Country 6	3.2	0.61	≈ 1.078 ✅
Country 7	0.7	-0.11	≈ 1.025 ✅
Country 8	1.2	0.71	≈ 1.03 ✅

All ratios are > 1 ⇒ GDP per capita increases for all countries.

✅ Answer: 0 countries

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